No, alot of people are wrong about this one. One thing you have to remember about Amaterasu is that Amaterasu is a jutsu and like all other jutsu it follows the laws of jutsu.
What has been said about 2 similar jutsu is that they will cancel each other out if and only if the same amount of chakra was put behind them, if one of the similar jutsu's have more chakra put behind them than the other jutsu then it will overpower and partly absorb the other jutsu causing it to deal even more damage to the power who put less chakra into there jutsu.
This is interesting because highly skilled ninja are good at chakra control and can use less and less chakra in order to use a jutsu but the draw back to that is that if someone uses the same jutsu against them but doesnt have as much chakra control, thus they need to use up more chakra in order to use the same jutsu, then there jutsu will eat up the skilled ninjas jutsu and deal more damage to them as well. This is what makes the Sharingan user so powerful, he can copy jutsu as you use them and depending on how much chakra he see's you using he can put in a bit more.
I wanted to pull up a scan of Kakahsi's fight against Zabuza as proof for this since it would be the perfect example but I am way too lazy to do that right now, im sure you all get what I am saying anyways.
Can Rasengan beat Rasengan?
The same concept will be applied to the Rasengan, which ever user puts more chakra into there rasengan will come out the victor with there rasengan gaining even more power by eating up the other rasengan thus dealing even more damage to the enemy ninja.
